Forward Kinematics Analysis of Parallel Robots Using Global Newton-Raphson Method

A new method, Global Newton-Raphson (GNR), for forward kinematics analysis of six degree-of-freedom (DOF) parallel robots is proposed, in order to obtain direct solutions of parallel robots in real time without divergence. The parallel robot can produce 3-DOF linear motions and 3-DOF angular motions, and feeds back positions of actuators measured by position sensors in real time. The GNR for the robot is built by Taylor series expansion and Newton-Raphson iteration with descent operator. Applying the GNR, the real generalized pose of moving platform is solved with respect to the base for a set of given positions of actuators. Accuracy and real time property of the GNR for the 6-DOF parallel robot are analyzed. The theoretical analysis indicated that the presented method can achieve the numerical convergent solution in real time with high accuracy, even the initial guesses are far from a solution.